I have a Thecus N8800+ NAS. It has 8 2TB drives and is RAID 6. One of the drives recently has been reported as having bad blocks, though the RAID is still reported as healthy.

I want to replace the drive before it fails, but I have never administered a NAS before. How do I replace the drive and maintain data integrity? Can I just pull out the drive and replace it while things are running or do I need to shut it down somehow? How will the RAID rebuild after I replace the drive?

On page 117 of the manual it lists the process here.
It appears you can just pull out the drives hot and it will auto-rebuild the RAID.

Replacing Damaged Hard Drives
If you are using RAID 1, RAID 5, or RAID 6 you can easily replace a damaged hard
drive in the Thecus N8800 while keeping your data secure with the system’s
automatic data recovery.
Hard Drive Damage
When a hard drive is damaged and data in the RAID volume, the system LCD will
display warning message also the system beeps.
Replacing a Hard Drive
RAID Auto-Rebuild
When using RAID 1, 5, 6, or 10 on the N8800, you can use the auto-rebuild function
when an error is detected.
4. The system automatically recognizes the new hard disk and starts the
auto-rebuild sequence to resume its status before the hard disk crash.

I have to go with the comment on reading the manual here - "RTFM" is normally an answer we avoid here, but when it comes to replacing disks in a RAID it is a very good idea to do so to make sure you know how your particular device's RAID controller will behave.
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RobMJan 30 '11 at 17:04